A global positioning system (GPS) receiver acquires and then tracks a GPS signal. After acquiring the GPS signal while in an acquisition mode, the GPS receiver then operates in a tracking mode where the carrier frequency and code phase of the signal are estimated using the Costas Loop and Delay Lock Loop, respectively. The power level of a GPS signal is typically very low (−130 dBm), which makes the signal susceptible to jamming or environmental blockage. When the carrier power-to-noise density (C/N0) of the GPS signal drops below a threshold level the receiver is forced to exit tracking mode. Once the C/N0 ratio of the GPS signal again exceeds the threshold the receiver must re-enter acquisition mode to reacquire the GPS signal.
Furthermore, the carrier tracking loop can lose lock due to user dynamics, unless the loop's order is greater than two, which is not unconditionally stable. Doppler-aiding refers to techniques that provide an estimate of the Doppler shift to the carrier tracking loop. There are two traditional Doppler-aiding solutions: 1) vector processing and 2) integration of GPS with an inertial measurement unit (IMU). Vector processing estimates the Doppler shift in the weak (low C/N0) tracking channel by using the stronger channels. However, this method only works if at least four channels with high C/N0 values are available. The integration of GPS with an IMU involves the integration of inertial sensors in a tight integration scheme using the extended Kalman filter. However, without high quality, expensive sensors, the deep integration method is not viable for periods of GPS outages more than tens of seconds. Also, due to the inherent nature of the Kalman filter, accurate modeling of the error sources is required. There exists a need for an accurate, cost-effective means of predicting the Doppler shift in GPS receivers.